Added verticality checks for g4 fluxes and changed zero section methods

docs/oscar_references.bib

@@ -1654,6 +1654,15 @@ @PhDThesis{Lev05
   school        = {Technische Universität Kaiserslautern}
 }
 
+@PhDThesis{Lin16,
+  author        = {Ling, Lin},
+  title         = {Gauge Fluxes in F-theory Compactifications},
+  year          = {2016},
+  doi           = {10.11588/heidok.00021601},
+  type          = {doctoralthesis},
+  school        = {Heidelberg U.}
+}
+
 @Book{Liu06,
   author        = {Liu, Qing},
   title         = {Algebraic geometry and arithmetic curves. Transl. by Reinie Erné},

experimental/FTheoryTools/docs/src/literature.md

@@ -99,6 +99,7 @@ following methods:
 * `has_weighted_resolution_generating_sections(m::AbstractFTheoryModel)`,
 * `has_weighted_resolution_zero_sections(m::AbstractFTheoryModel)`,
 * `has_zero_section(m::AbstractFTheoryModel)`,
+* `has_zero_section_coordinates(m::AbstractFTheoryModel)`,
 * `has_gauge_algebra(m::AbstractFTheoryModel)`,
 * `has_global_gauge_quotients(m::AbstractFTheoryModel)`.
 

experimental/FTheoryTools/src/AbstractFTheoryModels/attributes.jl

@@ -1013,10 +1013,10 @@ end
 
 
 @doc raw"""
-    zero_section(m::AbstractFTheoryModel)
+    zero_section_coordinates(m::AbstractFTheoryModel)
 
-Return the zero section of the given model.
-If no zero section is known, an error is raised.
+Return the zero section coordinates of the given model.
+If no zero section coordinates are known, an error is raised.
 This information is not typically stored as an attribute for
 Weierstrass and global Tate models, whose zero sections are known.
 
@@ -1026,13 +1026,35 @@ Assuming that the first row of the given grading is the grading under Kbar
 
 Hypersurface model over a not fully specified base
 
-julia> zero_section(h)
+julia> zero_section_coordinates(h)
 3-element Vector{QQMPolyRingElem}:
  0
  1
  0
 ```
 """
+function zero_section_coordinates(m::AbstractFTheoryModel)
+  @req has_zero_section_coordinates(m) "No zero section coordinates stored for this model"
+  return get_attribute(m, :zero_section_coordinates)
+end
+
+
+@doc raw"""
+    zero_section(m::AbstractFTheoryModel)
+
+Return the zero section of a model as a cohomology class in the toric ambient space.
+If no zero section is known, an error is raised.
+This information is not typically available for
+Weierstrass and global Tate models, whose zero sections are known.
+
+```jldoctest
+julia> qsm_model = literature_model(arxiv_id = "1903.00009", model_parameters = Dict("k" => 4))
+Hypersurface model over a concrete base
+
+julia> zero_section(qsm_model)
+Cohomology class on a normal toric variety given by x32 + 2*x33 + 3*x34 + x35 - x36
+```
+"""
 function zero_section(m::AbstractFTheoryModel)
   @req has_zero_section(m) "No zero section stored for this model"
   return get_attribute(m, :zero_section)

experimental/FTheoryTools/src/AbstractFTheoryModels/methods.jl

@@ -634,10 +634,19 @@ function set_weighted_resolution_zero_sections(m::AbstractFTheoryModel, vs::Vect
   set_attribute!(m, :weighted_resolution_zero_sections => result)
 end
 
-function set_zero_section(m::AbstractFTheoryModel, desired_value::Vector{String})
+function set_zero_section_coordinates(m::AbstractFTheoryModel, desired_value::Vector{String})
   R, _ = polynomial_ring(QQ, collect(keys(explicit_model_sections(m))), cached = false)
   f = hom(R, cox_ring(base_space(m)), collect(values(explicit_model_sections(m))))
-  set_attribute!(m, :zero_section => [f(eval_poly(l, R)) for l in desired_value])
+  set_attribute!(m, :zero_section_coordinates => [f(eval_poly(l, R)) for l in desired_value])
+end
+
+function set_zero_section(m::AbstractFTheoryModel, desired_value::String)
+  divs = torusinvariant_prime_divisors(ambient_space(m))
+  cohomology_ring(ambient_space(m); check=false)
+  cox_gens = string.(gens(cox_ring(ambient_space(m))))
+  @req desired_value in cox_gens "Specified zero section is invalid"
+  index = findfirst(x -> x==desired_value, cox_gens)
+  set_attribute!(m, :zero_section => cohomology_class(divs[index]))
 end
 
 function set_gauge_algebra(m::AbstractFTheoryModel, algebras::Vector{String})

experimental/FTheoryTools/src/AbstractFTheoryModels/properties.jl

@@ -96,6 +96,7 @@ has_weighted_resolutions(m::AbstractFTheoryModel) = has_attribute(m, :weighted_r
 has_weighted_resolution_generating_sections(m::AbstractFTheoryModel) = has_attribute(m, :weighted_resolution_generating_sections)
 has_weighted_resolution_zero_sections(m::AbstractFTheoryModel) = has_attribute(m, :weighted_resolution_zero_sections)
 has_zero_section(m::AbstractFTheoryModel) = has_attribute(m, :zero_section)
+has_zero_section_coordinates(m::AbstractFTheoryModel) = has_attribute(m, :zero_section_coordinates)
 has_gauge_algebra(m::AbstractFTheoryModel) = has_attribute(m, :gauge_algebra)
 has_global_gauge_quotients(m::AbstractFTheoryModel) = has_attribute(m, :global_gauge_quotients)
 

experimental/FTheoryTools/src/G4Fluxes/properties.jl

@@ -14,7 +14,7 @@ for any two toric divisors $D_1$, $D_2$. If all of these
 simple consistency checks are met, this method will return
 `true` and otherwise `false`.
 
-It is worth mentioning that currently (July 2024), we only
+It is worth mentioning that currently (August 2024), we only
 support this check for $G_4$-fluxes defined on Weierstrass,
 global Tate and hypersurface models. If this condition is not
 met, this method will return an error.
@@ -42,7 +42,7 @@ true
 
   # Compute the cohomology class corresponding to the hypersurface equation
   cy = polynomial(cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))))
-
+  
   # Now check quantization condition G4 + 1/2 c2 is integral.
   c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))]
 
@@ -52,9 +52,67 @@ true
   # now execute elementary checks of the quantization condition
   for i in 1:length(c_ds)
     for j in i:length(c_ds)
-      numb = integrate(cohomology_class(ambient_space(m), twist_g4 * cy * c_ds[i] * c_ds[j]); check = false)
+      numb = integrate(cohomology_class(ambient_space(m), twist_g4 * c_ds[i] * c_ds[j] * cy); check = false)
       !is_integer(numb) && return false
     end
   end
   return true
 end
+
+
+@doc raw"""
+    passes_verticality_checks(gf::G4Flux)
+
+G4-fluxes are subject to verticality conditions described in [Lin16](@cite).
+It is hard to verify that these condition are met. However,
+we can execute a number of simple consistency checks, by
+verifying that $\int_{Y}{G_4 \wedge [D_1] \wedge [zero section]} = 0$ and $\int_{Y}{G_4 \wedge [D_1] \wedge [D_2]} = 0$
+for all toric base divisors $D_1$ and $D_2$. If all of these
+simple consistency checks are met, this method will return
+`true` and otherwise `false`
+
+```jldoctest
+julia> qsm_model = literature_model(arxiv_id = "1903.00009", model_parameters = Dict("k" => 4))
+Hypersurface model over a concrete base
+
+julia> divs = torusinvariant_prime_divisors(ambient_space(qsm_model));
+
+julia> e1 = cohomology_class(divs[35]);e2 = cohomology_class(divs[32]);e4 = cohomology_class(divs[34]);u = cohomology_class(divs[33]);v = cohomology_class(divs[30]);pb_Kbar = cohomology_class(sum([divs[k] for k in 1:29]));
+
+julia> g4_class = (-3) // kbar3(qsm_model) * (5 * e1 * e4 + pb_Kbar * (-3 * e1 - 2 * e2 - 6 * e4 + pb_Kbar - 4 * u + v))
+Cohomology class on a normal toric variety given by 1//2*x5*x32 + x5*x33 + 3//2*x5*x34 + x5*x35 + 1//2*x5*x36 + 1//2*x6*x32 + x6*x33 + 3//2*x6*x34 + x6*x35 + 1//2*x6*x36 - x7*x12 + 1//2*x7*x32 + x7*x33 + 3//2*x7*x34 + x7*x35 + 1//2*x7*x36 - 4*x8*x23 - 2*x10*x23 + 2*x15*x26 + 1//2*x15*x32 + x15*x33 + 3//2*x15*x34 + x15*x35 + 1//2*x15*x36 + x16^2 + 1//2*x16*x32 + x16*x33 + 3//2*x16*x34 + x16*x35 + 1//2*x16*x36 + 11*x17*x24 + x17*x32 + 2*x17*x33 + 3*x17*x34 + 2*x17*x35 + x17*x36 + 5*x18^2 - 7//4*x18*x25 + x18*x32 + 2*x18*x33 + 3*x18*x34 + 2*x18*x35 + x18*x36 + 3//2*x19*x32 + 3*x19*x33 + 9//2*x19*x34 + 3*x19*x35 + 3//2*x19*x36 - 4*x20^2 - 44//3*x20*x21 + 7//2*x20*x25 + x20*x32 + 2*x20*x33 + 3*x20*x34 + 2*x20*x35 + x20*x36 - 11//6*x21^2 + 77//6*x21*x24 + x21*x32 + 2*x21*x33 + 3*x21*x34 + 2*x21*x35 + x21*x36 - 31//6*x22^2 - 5//6*x22*x23 - 97//12*x22*x25 - 2*x23^2 + 4*x24^2 + 17//6*x24*x27 + 1//2*x24*x32 + x24*x33 + 3//2*x24*x34 + x24*x35 + 1//2*x24*x36 - 7//4*x25^2 + 1//2*x25*x32 + x25*x33 + 3//2*x25*x34 + x25*x35 + 1//2*x25*x36 + 1//3*x26*x27 - 5//6*x27^2 + 1//2*x27*x32 + x27*x33 + 3//2*x27*x34 + x27*x35 + 1//2*x27*x36 - 1//2*x28^2 + 7//6*x29^2 - 5//2*x35*x36
+
+julia> g4 = g4_flux(qsm_model, g4_class, check = false)
+G4-flux candidate lacking elementary quantization checks
+
+julia> passes_verticality_checks(g4)
+true
+```
+"""
+@attr Bool function passes_verticality_checks(g4::G4Flux)
+  m = model(g4)
+  @req (m isa WeierstrassModel || m isa GlobalTateModel || m isa HypersurfaceModel) "Verticality checks for  G4-fluxes only supported for Weierstrass, global Tate and hypersurface models"
+  @req base_space(m) isa NormalToricVariety "Verticality checks for G4-flux currently supported only for toric base"
+  @req ambient_space(m) isa NormalToricVariety "Verticality checks for G4-flux currently supported only for toric ambient space"
+  @req has_zero_section(m) "For verticality checks, a model zero section needs to be specified"
+
+  # Compute the cohomology class corresponding to the hypersurface equation
+  cy = polynomial(cohomology_class(toric_divisor_class(ambient_space(m), degree(hypersurface_equation(m)))))
+
+  n = length(gens(cox_ring(base_space(m))))
+  c_ds = [polynomial(cohomology_class(d)) for d in torusinvariant_prime_divisors(ambient_space(m))[1:n]]
+  zero_sec = zero_section(m)
+
+  # now execute verticality checks
+  for i in 1:n
+    numb = integrate(cohomology_class(ambient_space(m), polynomial(cohomology_class(g4)) * c_ds[i] * cy) * zero_sec; check = false)
+    numb!=0 && return false
+  end
+  for i in 1:n
+    for j in i:n
+      numb = integrate(cohomology_class(ambient_space(m), polynomial(cohomology_class(g4)) * c_ds[i] * c_ds[j] * cy); check = false)
+      numb!=0 && return false
+    end
+  end
+  return true
+end

experimental/FTheoryTools/src/LiteratureModels/Models/model1208_2695-1.json

@@ -54,7 +54,7 @@
             [1, 1, 0]
         ],
         "hypersurface_equation": "w^2 + b * v^2 * w - u * (c0 * u^3 + c1 * u^2 * v + c2 * u * v^2 + c3 * v^3)",
-        "zero_section": ["0", "1", "0"],
+        "zero_section_coordinates": ["0", "1", "0"],
         "generating_sections": [["0", "1", "-b"]]
     },
     "birational_models": ["model1208_2695-2.json"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1,  2, -1, 0, -1],
             [-1, -1, -1, -1,  0, 0,  1]
         ],
-        "zero_section": ["0", "0", "1"]
+        "zero_section_coordinates": ["0", "0", "1"]
     },
     "associated_models": [
         "model1408_4808-1-WSF.json",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-10.json

@@ -62,7 +62,7 @@
             [-1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*e3^6*u^3 + s2*e1^2*e2^3*e3^4*u^2*v + s3*e1^2*e2^2*e3^2*u*v^2 + s4*e1^2*e2*v^3 + s5*e1*e2^2*e3^3*u^2*w + s6*e1*e2*e3*u*v*w + s8*u*w^2",
-        "zero_section": ["s4", "1", "1", "1", "-s8", "0"]
+        "zero_section_coordinates": ["s4", "1", "1", "1", "-s8", "0"]
     },
     "associated_models": [
         "model1408_4808-1.json",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, -1, 0, 0],
             [-1, -1, -1,  0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 + s9^5*(8*s2*s5^2 - 12*s1*s6*s5) + s5^2*s6^2*s9^4)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-11.json

@@ -63,7 +63,7 @@
             [ 1,  1, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4^4*u^3 + s2*e1*e2^2*e3^2*e4^2*u^2*v + s3*e2^2*e3^3*u*v^2 + s5*e1^2*e2*e4^3*u^2*w + s6*e1*e2*e3*e4*u*v*w + s9*e1*v*w^2",
-        "zero_section": ["1", "0", "s5", "1", "1", "-s5", "1"],
+        "zero_section_coordinates": ["1", "0", "s5", "1", "1", "-s5", "1"],
         "generating_sections": [
             ["s9", "1", "1", "-s3", "1", "1", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0, -1, 0, 1, 0],
             [-1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 - 4*s2*s9)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-12.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s2*e1*e2^2*e3^2*u^2*v + s5*e1^2*e2*e4^2*u^2*w + s6*e1*e2*e3*e4*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*e4^2*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1"],
         "generating_sections": [
             ["1", "s5", "1", "1", "-s9", "0", "1"],
             ["1", "1", "s2", "-s7", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1, 0, 0],
             [-1, -1, -1, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "torsion_sections": [
             ["1//12*(s6^2 - 4*s2*s9)", "0", "1"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-13.json

@@ -63,7 +63,7 @@
             [1,  1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e5^4*u^3 + s2*e1*e2^2*e3^2*e4^2*e5^2*u^2*v + s3*e2^2*e3^3*e4^4*u*v^2 + s6*e1*e2*e3*e4*e5*u*v*w + s9*e1*v*w^2",
-        "zero_section": ["1", "s1", "1", "1", "1", "-s9", "0", "1"],
+        "zero_section_coordinates": ["1", "s1", "1", "1", "1", "-s9", "0", "1"],
         "torsion_sections": [
             ["s9", "1", "1", "-s3", "1", "1", "1", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14-WSF.json

@@ -55,7 +55,7 @@
             [-1, -1, 0, 1, 0],
             [-1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 - s5^2*s9^4*( - s6^2 + 4*s5*s7) - 12*s1*s5*s6*s9^5)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-14.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s5*e1^2*e2*e4^2*e5^2*u^2*w + s6*e1*e2*e3*e4*e5*u*v*w + s7*e2*e3^2*v^2*w + s9*e1*e4^2*e5^3*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
         "generating_sections": [
             ["1", "1", "s1", "1", "1", "1", "-s7", "0"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15-WSF.json

@@ -55,7 +55,7 @@
             [0, -1, 0, 1, 0],
             [-1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             ["1//12*(8*s2*s5^2*s9^5 - s5^2*s9^4*( - s6^2 + 4*s5*s7))", " -1//2*s2*s5^3*s6*s9^7", "s5*s9^2"]
         ],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-15.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s2*e1*e2^2*e3^2*u^2*v + s5*e1^2*e2*e4^2*u^2*w + s6*e1*e2*e3*e4*e5*u*v*w + s7*e2*e3^2*e5^2*v^2*w + s9*e1*e4^2*e5^2*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1", "1"],
         "generating_sections": [
             ["1", "1", "s2", "-s7", "1", "1", "0", "1"]
         ],

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16-WSF.json

@@ -55,7 +55,7 @@
             [-1, 0, 1, 0],
             [-1, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "torsion_sections": [
             ["1//12*s6^2", "1//2*s1*s7*s9", "1"],
             ["1//12*s6^2", "-1//2*s1*s7*s9", "1"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-16.json

@@ -63,7 +63,7 @@
             [1, 1, 0, 0, 0, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^2*e3*e4*u^3 + s6*e1*e2*e3*e4*e5*e6*u*v*w + s7*e2*e3^2*e6^3*v^2*w + s9*e1*e4^2*e5^3*v*w^2",
-        "zero_section": ["0", "1", "1", "s7", "-s9", "1", "1", "1", "1"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "-s9", "1", "1", "1", "1"],
         "torsion_sections": [
             ["1", "1", "s1", "1", "1", "1", "-s7", "0", "1"],
             ["1", "s1", "1", "1", "1", "-s9", "1", "1", "0"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1,  2, -1, 0, 1, -1, 0],
             [-1, -1, -1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(12*s1^2*s9^6 + 4*(2*s2*(s5^2 - 3*s1*s8) - 3*s1*s5*s6)*s9^5 + ((s6^2 - 4*s5*s7)*s5^2 + 12*(s2^2 + 2*s1*s3)*s8^2 - 4*(4*s3*s5^2 + s2*s6*s5 - 3*s1*(s6^2 + 2*s5*s7))*s8)*s9^4 - 2*s8*( - 4*(s6*s7 + 3*s4*s8)*s5^2 + (s6^3 - 10*s3*s8*s6 + 4*s2*s7*s8)*s5 + 2*s8*(9*s1*s6*s7 + 6*s1*s4*s8 + s2*(s6^2 + 6*s3*s8)))*s9^3 + s8^2*(s6^4 - 2*s5*s7*s6^2 - 8*s5^2*s7^2 + 12*(s3^2 + 2*s2*s4)*s8^2 - 4*(9*s4*s5*s6 - s7*(5*s2*s6 + 6*s1*s7) + s3*(s6^2 + 2*s5*s7))*s8)*s9^2 - 2*s8^3*(12*s3*s4*s8^2 + 2*(s7*(s3*s6 + 4*s2*s7) - 3*s4*(s6^2 + 2*s5*s7))*s8 + s6*s7*(s6^2 - 4*s5*s7))*s9 + s8^4*((s6^2 - 4*s5*s7)*s7^2 + 4*(2*s3*s7 - 3*s4*s6)*s8*s7 + 12*s4^2*s8^2))",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-3.json

@@ -62,7 +62,7 @@
             [1, 1, 0, 0]
         ],
         "hypersurface_equation": "s1*u^3*e1^2 + s2*u^2*v*e1^2 + s3*u*v^2*e1^2 + s4*v^3*e1^2 + s5*u^2*w*e1 + s6*u*v*w*e1 + s7*v^2*w*e1 + s8*u*w^2 + s9*v*w^2",
-        "zero_section": ["s9", "-s8", "1", "0"],
+        "zero_section_coordinates": ["s9", "-s8", "1", "0"],
         "generating_sections": [
             ["-s9", "s8", "s1 * s9^3 - s4 * s8^3 + s3 * s9 * s8^2 - s2 * s9^2 * s8", "s7 * s8^2 - s6 * s9 * s8 + s5 * s9^2"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5-WSF.json

@@ -54,7 +54,7 @@
             [-1,  0,  1, -1, 0, 1, -1, 0],
             [-1, -1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2 - 4*s5*s7 + 8*s3*s8 - 4*s2*s9)",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-5.json

@@ -62,7 +62,7 @@
             [1, 1, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e2^2*e1^2*u^3 + s2*e2^2*e1*u^2*v + s3*e2^2*u*v^2 + s5*e2*e1^2*u^2*w + s6*e2*e1*u*v*w + s7*e2*v^2*w + s8*e1^2*u*w^2 + s9*e1*v*w^2",
-        "zero_section": ["s9", "-s8", "1", "1", "0"],
+        "zero_section_coordinates": ["s9", "-s8", "1", "1", "0"],
         "generating_sections": [
             ["s7", "1", "-s3", "0", "1"],
             ["0", "1", "1", "s7", "-s9"]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6-WSF.json

@@ -55,7 +55,7 @@
             [-1,  0,  1,  2, -1, 0, 1, -1],
             [-1, -1, -1, -1,  0, 0, 0, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s8^4*(12*s4^2*s8^2 - s7^2*( - s6^2 + 4*s5*s7) + s7*s8*(8*s3*s7 - 12*s4*s6)))",

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-6.json

@@ -63,7 +63,7 @@
             [1,  1, 0, 0, 0]
         ],
         "hypersurface_equation": "s1*e1^2*e2^4*u^3 + s2*e1^2*e2^3*u^2*v + s3*e1^2*e2^2*u*v^2 + s4*e1^2*e2*v^3 + s5*e1*e2^2*u^2*w + s6*e1*e2*u*v*w + s7*e1*v^2*w + s8*u*w^2",
-        "zero_section": ["-s7", "1", "s8", "1", "0"],
+        "zero_section_coordinates": ["-s7", "1", "s8", "1", "0"],
         "generating_sections": [
             ["0", "1", "s4", "1", "-s7"]
         ]

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7-WSF.json

@@ -54,7 +54,7 @@
             [0,  1, -1, 0, 1, -1, 0],
             [-1, -1,  0, 0, 0, 1, 1]
         ],
-        "zero_section": ["0", "0", "1"],
+        "zero_section_coordinates": ["0", "0", "1"],
         "generating_sections": [
             [
                 "1//12*(s6^2*s7^2 - 4*s5*s7^3 + 8*s3*s7^2*s8 - 12*s3*s6*s7*s9 + 8*s2*s7^2*s9 + 12*s3^2*s9^2)", 

experimental/FTheoryTools/src/LiteratureModels/Models/model1408_4808-7.json

@@ -62,7 +62,7 @@
             [1, 1, 0, 0, 0, 0]
         ],
         "hypersurface_equation": "s2*e1*e3^2*u^2*v + s3*e2*e3^2*u*v^2 + s5*e1^2*e3*u^2*w + s6*e1*e2*e3*u*v*w + s7*e2^2*e3*v^2*w  + s8*e1^2*e2*u*w^2 + s9*e1*e2^2*w^2*v",
-        "zero_section": ["0", "1", "1", "s7", "1", "-s9"],
+        "zero_section_coordinates": ["0", "1", "1", "s7", "1", "-s9"],
         "generating_sections": [
             ["s7", "1", "-s3", "0", "1", "1"],
             ["1", "s5", "-s2", "1", "0", "1"],